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  • Research Article
  • Open Access

Space-Varying Iterative Restoration of Diffuse Optical Tomograms Reconstructed by the Photon Average Trajectories Method

  • 1Email author,
  • 1,
  • 2 and
  • 3
EURASIP Journal on Advances in Signal Processing20072007:034747

  • Received: 2 February 2006
  • Accepted: 29 October 2006
  • Published:


The possibility of improving the spatial resolution of diffuse optical tomograms reconstructed by the photon average trajectories (PAT) method is substantiated. The PAT method recently presented by us is based on a concept of an average statistical trajectory for transfer of light energy, the photon average trajectory (PAT). The inverse problem of diffuse optical tomography is reduced to a solution of an integral equation with integration along a conditional PAT. As a result, the conventional algorithms of projection computed tomography can be used for fast reconstruction of diffuse optical images. The shortcoming of the PAT method is that it reconstructs the images blurred due to averaging over spatial distributions of photons which form the signal measured by the receiver. To improve the resolution, we apply a spatially variant blur model based on an interpolation of the spatially invariant point spread functions simulated for the different small subregions of the image domain. Two iterative algorithms for solving a system of linear algebraic equations, the conjugate gradient algorithm for least squares problem and the modified residual norm steepest descent algorithm, are used for deblurring. It is shown that a gain in spatial resolution can be obtained.


  • Deblurring
  • Steep Descent
  • Point Spread Function
  • Linear Algebraic Equation
  • Gradient Algorithm

Authors’ Affiliations

Russian Federal Nuclear Centre, Institute of Technical Physics, P.O. Box 245, Snezhisk Chelyabinsk Region, 456770, Russia
Institute of Electronic Structure and Laser, Foundation for Research and Technology — Hellas, P.O. Box 1527, Vassilika Vouton, Heraklion, 71110, Greece
Research Institute for Laser Physics, 12 Birzhevaya Lin, Saint Petersburg, 199034, Russia


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© Konovalov et al. 2007